1)Energy stored in the ball

to find the potential energy it should be with respect to two things

like for eg.potential energy between the ball and the earth

to find kinetic energy the ball should be moving...

total energy is the sum of potential and kinetic!!!

The above post is right in suggesting that you add the potential and kinetic energies, but form the question it seems that the electrostatic potential energy is being asked for rather than the mechanical. Assuming this is true, u can find the electrostatic potential energy by proceeding this way: find a general expression for the energy required to bring  'n' unit differential charge from infinity to the surface of the sphere when it already has 'n-1' unit differential charge in it. Then, integrate it from n=1 to n=Q .You may be able to reduce it to as easier series sum or something similar... I haven't actually tried. 

That will give you the electrostatic potential energy of the given charge configuration of Q charge spread uniformly on the surface of a sphere. Regarding the energy of the surroundings, it is not clear what id meant by the term, but you can try this:: Find an expression for the electric field from the surface outwards, and then integrate it in three dimensions to get the total value of the electric field. Then u get the energy of the 'surroundings' due to the electric field by using E=0.5(epsilon zero) (electric field square) ... The idea is to find the TOTAL electric field  somehow and then use the above equation. However, there is a catch here: If by 'surroundings' u mean the entire infinite universe, then that 'surrounding also includes you, and the work done by you to out the charges into that configuration has to be taken into account and ultimately, the energy of the surroundings will turn out to be the numerical negative of the energy obtained in part 1 of your question, that is the energy stored in the ball. This is because all the energy stored in the ball must have come from its surroundings and thus, the gain(or loss) of energy if the ball must be compensated by an exact loss (or gain) in the surroundings. 

Following the above two directions of approach, in the first case, where you calculate the total electric field, the total energy of the surroundings and the ball will be the sum of the answers to part 1 and 2 of your question. However, going with the second approach, that is taking the entire universe as the surrounding, we come to total energy=0. This might look odd, but remember that energy is a relatively measured quantity. We can choose any suitable 'zero' level for the energy of a system and calculate the changes accordingly. In this case, while calculating the electrostatic potential energy of the system in part 1, we had arbitraryly chosen the infinity as the 'zero' level for the charge configuration, and hence we came out with this result. In we had chosen some other arbitrary value, we may come to some other value. Or we may even like to shift all our calculation by some places on the number line and end up on any value of the energy. The value of arbitrary.

I hope that helps.

I like the above Explanation but ......

Even if it is electrostatic energy we have to state it with reference to two objects...

For eg.The P.E. between the ball and the earth is 5J is right..

The P.E. of the ball is 5J is wrong...